Question

$If\overline{a}.\overline{b}=\overline{a}.\overline{c}and\overline{a}\ne \overline{0},thenwecansaythat\overline{b}=\overline{c}.$

• A. True
• B. False

Answer 1

The correct option is B

False

$\overline{a}.\overline{b}=\overline{c}$ can be written as $\overline{a}.(\overline{b}-\overline{c})=\overline{0}$

(Using distributive law which is valid for dot product).

Now this will imply the following

either $\overline{b}=\overline{c}or\overline{a}$ is perpendicular to $(\overline{b}-\overline{c})$

The reason behind $\overline{a}$ is perpendicular to $\overline{b}-\overline{c}$ is that dot product between two vectors is zero when the angle between them is ${90}^{\circ }$ (cos ${90}^{\circ }$ = 0).